Some types of wireless networks, in particular those that operate in the 60 GHz bands, use directional communications to mitigate intra-network and inter-network interference between devices. The directionality of the transmissions and receptions are typically achieved through the use of multi-antenna phased arrays. To achieve directionality in a particular direction, such arrays are ‘trained’ by transmitting a known pattern, and processing the resultant signals received at each antenna of the receiving device to determine the parameters to use to achieve directionality in that particular direction. If the devices are mobile, new antenna training may be frequently required to adjust the desired directionality by determining new parameters. Although coarse antenna training procedures are available, to achieve high data rates fine antenna training must be done, and currently defined protocols do not provide an efficient process for doing this.